Find the angles of an isosceles trapezoid if one of its angles is 30 ° greater than the other.

Given:
ABCE – isosceles trapezoid,
angle A = angle B + 30 degrees.
Find the degree measures of the angles of the parallelogram ABCE: angle A, angle B, angle C, angle E -?
Solution:
Consider an isosceles trapezoid ABCE. Its angles at the base are equal to each other, then angle A = angle E, angle B = angle C.
Let the degree measure of angle B be equal to x degrees, then the degree measure of angle A is equal to x + 30 degrees. We know that the sum of the degree measures of a parallelogram is 360 degrees. Let’s make the equation:
x + x + x + 30 + x + 30 = 360;
x + x + x + x + 60 = 360;
x + x + x + x = 360 – 60;
x + x + x + x = 300;
x * (1 + 1 + 1 + 1) = 300;
x * 4 = 300;
x = 300: 4;
x = 75 degrees – the degree measure of the angle B;
30 + 75 = 105 degrees is the degree measure of angle A.
Answer: 105 degrees; 75 degrees; 75 degrees; 105 degrees.